Here is the world as we know it at its beginning, after the Flood, through the family of Noah. Now we begin to see the breaking of those families into a variety of parts, each of which became a nation of itself, so we see:
Then the Bible follows Arphaxad's line, and when we get down to verse 24:
These two chapters show very clearly that Israel, who came out of the line of Shem through Arphaxad, through Eber, through Terah, through Abraham, had its roots in the world. However, chapter 11 interjects something between verses 1 and 10 showing the alienation of these nations of mankind from God. These are all the nations that came from Noah through Shem, Ham, and Japheth, who were caused to live under a curse, being scattered across the face of the earth, indicating that they were away from the presence of the God, and therefore, the blessings of God.
As we finish chapter 11, it is immediately followed by the calling and separation of Abram in Genesis 12.
Shem gave birth to Arphaxad then in verse 16, Arphaxad's line gave birth to Eber, then six generations later, Abraham was born. Of course he became the one that God called out of the land of the Chaldees and he is the one who became the father of the faithful.
I will turn to a verse in the book of Hebrews, and I think that since we are going into Babylonia, it is very interesting that God should make this little remark about Abraham. We will see this to be important later on.
In fact Shem's son Arphaxad, whom we see in the list of Shem's descendants (specifically I am looking at the one in in Genesis 11:10), was not the firstborn. If you go back to Genesis 10:22, you find that the sons of Shem were Elam, Asshur, Arphaxad, Lud, and Aram. So evidently, if this list is going to be believed as the proper birth order, Arphaxad was the third born, not the first.